Abstract:
The problem with transportation is figuring out how much has to be carried
from each source to each destination to maintain the total cost of transportation
as minimal as possible while still satisfying supply and demand constraints.
The Transportation Problem (TP) is concerned with choosing routes to
distribute the goods to the various destinations to either minimize the overall
transportation cost or maximize the overall revenue of the problem by
satisfying the needs of the various destinations and supplying quantities from
various sources. Many approaches to solving TP have been developed in the
literature. In TP, two-step procedures are possible, including an Initial
Feasible Solution (IFS) and an Optimal Solution (OS). For the TP, an OS may
be found using the Modified Distribution (MODI) Method or the Stepping
Stone Method, and an IFS can be found using the North-West Corner Method
(NWCM), the Least Cost Method (LCM), and Vogel's Approximation Method
(VAM), and so on. In this study, a novel procedure for identifying an initial
feasible solution to both balanced and unbalanced TP is examined using the
penalty cost method. To determine the optimal or near-optimal solution for
TP, the suggested method could be used. The results can be compared to those
of other current algorithms.
